Abstract
The generalization performance is the main purpose of machine learning theoretical research. This note mainly focuses on a theoretical analysis of learning machine with negatively associated dependent input sequence. The explicit bound on the rate of uniform convergence of the empirical errors to their expected error based on negatively associated dependent input sequence is obtained by the inequality of Joag-dev and Proschan. The uniform convergence approach is used to estimate the convergence rate of the sample error of learning machine that minimize empirical risk with negatively associated dependent input sequence. In the end, we compare these bounds with previous results.
Supported in part by NSFC under grant 60403011.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bousquet, O., Elisseeff, A.: Stability and generalization. Journal of Machine Learning Research 2, 499–526 (2002)
Cucker, F., Smale, S.: On the mathematical foundations of learning. Bulletin of the American Mathematical Society 39, 1–49 (2002)
Forster, J., Warmuth, M.: Relative expected instantaneous loss bounds. Journal of Computer and System Science 64, 76–102 (2002)
Joag-dev, K., Proschan, F.: Negative associated of random variables with applications. Annals of Statistics 11, 286–295 (1983)
Karandikar, R.L., Vidyasagar, M.: Rates of uniform convergence of empirical means with mixing processes. Statist. Probab. Lett. 58, 297–307 (2002)
Nobel, A., Dembo, A.: A note on uniform laws of averages for dependent processes. Statist. Probab. Lett. 17, 169–172 (1993)
Vapnik, V.: Statistical Learning Theory. Wiley, New York (1998)
Vidyasagar, M.: Learning and Generalization with Applications to Neural Networks. Springer, London (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zou, B., Li, L., Xu, J. (2006). The Generalization Performance of Learning Machine with NA Dependent Sequence. In: Wang, GY., Peters, J.F., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2006. Lecture Notes in Computer Science(), vol 4062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11795131_82
Download citation
DOI: https://doi.org/10.1007/11795131_82
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36297-5
Online ISBN: 978-3-540-36299-9
eBook Packages: Computer ScienceComputer Science (R0)